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The emergence of $R^2$ (Starobinsky) inflation from the semi-classical modification of gravity due to matter quantum fields (trace anomaly) clearly points out the importance of fundamental physics and the first principles in the…
Noncommutative geometry can provide effective description of physics at very short distances taking into account generic effects of quantum gravity. Inflation amplifies tiny quantum fluctuations in the early universe to macroscopic scales…
In this chapter we review the recent developments of realizing $R^2$-like inflation in the framework of a most general UV nonlocal extension of Einstein's general theory of relativity (GR). It is a well-motivated robust approach towards…
The $R^2$ inflation which is an extension of general relativity (GR) by quadratic scalar curvature introduces a quasi-de Sitter expansion of the early Universe governed by Ricci scalar being an eigenmode of d'Alembertian operator. In this…
We investigate cosmological solutions for the modified gravity theory obtained from quantum relative entropy between the metric of spacetime and the metric induced by the geometry and matter fields. The vacuum equations admit inflationary…
Inflationary cosmology has proved to be the most successful at predicting the properties of the anisotropies observed in the cosmic microwave background (CMB). In this essay we show that quantum field renormalization significantly…
Measurements of CMB anisotropy and, more recently, polarization have played a very important role allowing precise determination of various parameters of the `standard' cosmological model. The expectation of the paradigm of inflation and…
Power spectra always play an important role in the theory of inflation. In particular, the ability to reproduce the galaxy matter power spectrum and the CMB temperature angular power spectrum coefficients to high accuracy is often…
It is natural to expect a consistent inflationary model of the very early Universe to be an effective theory of quantum gravity, at least at energies much less than the Planck one. For the moment, $R+R^2$, or shortly $R^2$, inflation is the…
Supersymmetry is the most natural framework for physics above the TeV scale, and the corresponding framework for early-Universe cosmology, including inflation, is supergravity. No-scale supergravity emerges from generic string…
Inflation provides a unified paradigm for understanding the isotropy of the cosmic microwave background (CMB), the flatness problem, and the origin of large-scale structure. Although the physics responsible for inflation is not yet well…
Recent results from cosmic microwave background (CMB) experiments verify several of the predictions of inflation, while ruling out a number of alternative structure-formation scenarios. Given the successes of the theory, the obvious next…
Informed by a quantum information perspective, we interpret cosmological expansion of space as growing entanglement between underlying degrees of freedom. In particular, we focus on inflationary cosmology, which, while being a successful…
Recent measurements of temperature fluctuations in the cosmic microwave background (CMB) indicate that the Universe is flat and that large-scale structure grew via gravitational infall from primordial adiabatic perturbations. Both of these…
In this article we review the theory of cosmological inflation with a particular focus on the beautiful connection it provides between the physics of the very small and observations of the very large. We explain how quantum mechanical…
Considering the inflation model based on a $f(R)$ gravity theory, we obtain several important constraints from the large angular scale CMBR observations. First, the ordinary slow-roll assumption during the inflation together with…
Current bounds from the polarization of the CMB predict the scale-invariant gravitational wave (GW) background of inflation to be out of reach for upcoming GW interferometers. This prospect dramatically changes if the inflaton is a…
We investigate the effects of non-zero spatial curvature on cosmic inflation in the light of cosmic microwave background (CMB) anisotropy measurements from the Planck 2018 legacy release and from the 2015 observing season of BICEP2 and the…
We review inflationary cosmology in modified gravity such as $R^2$ gravity with its extensions in order to generalize the Starobinsky inflation model. In particular, we explore inflation realized by three kinds of effects: modification of…
We consider the large-scale cosmic structure generation by an inflation based on a pure f(R)-type gravity theory. Comparison with recent CMBR observations gives the following results: (1) The near Zel'dovich spectral conditions uniquely…